QM Research Seminar: Noncritical strings, enumerative invariants and modularity

Speaker: Guglielmo Lockhart (Universität Bonn)



Abstract:

String theory compactification on elliptic Calabi-Yau manifolds provides a bridge between enumerative geometry on one side, and vertex operator algebras and a modular or Jacobi forms of various kinds on the other. This comes about because compactification leads to supersymmetric quantum field or quantum gravity theories that include two-dimensional objects, the noncritical strings, among their degrees of freedom. Exploiting this connection has led to a deeper understanding both of the spectrum of supersymmetric theories and of the modular properties of generating functions of enumerative invariants. In the first part of the talk I will give a broad overview of this subject, while in the second part I will focus on a recent work with Michele Del Zotto, where we find a link between Donaldson-Thomas invariants of higher rank, vector-valued Jacobi forms, and a two-dimensional analogue of Kronheimer-Nakajima quivers.